Precipitation Reaction and the Solubility

I.Introduction
In this experiment we can see precipitate by observing variety of reaction. Precipitation will occur by precipitation reaction this is a reaction that two or more solution reacts to produce a precipitate. Also, there are often double displacement reactions. For example solution of Lead(²U)nitrate and Potassium iodide react:
Pb(NO3)2(aq) + 2KI (aq) ¨ PbI2 (s) + 2KNO3 (aq)
You will see that PbI2 is the precipitate.
Now for example:
LI (aq) + Na(NO3)2 (aq) ¨ NO PRECIPITATE
You will see that there was no precipitate I this reaction. Then, what is the diff…